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The Moduli Space Metric for Well-Separated Non-Abelian Vortices
High Energy Physics - Theory · Submitted 24 Feb 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation.
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The abstract, sentence by sentence
The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation. | result 0.74 | 0.90 | 0.79 | asserted 1.00 |
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The paper
Original abstract
The moduli space metric and its Kahler potential for well-separated non-Abelian vortices are obtained in U(N) gauge theories with N Higgs fields in the fundamental representation.
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References
How the literature uses it
16 arXiv papers cite this in 33 sentences
Papers citing it · 20 sentences without a confident label
Contests it 1 paper
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On the other hand, it is shown that, although Hanany-Tong's approach can capture the global structure of the vortex moduli space, the local structure is not correctly treated: the metric of the moduli space is different from the result obtained from the purely field theoretical method [ref] .
Vortex counting from field theory · Introduction · contest 0.78
Uses its method or tool 3 papers
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In this paper we apply the moduli matrix approach to study the vortex moduli space [ref] .
Vortex counting from field theory · Introduction · 1.00
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By rewriting the gauge fields in terms of a matrix $S∈GL(N_c, ℂ)$ [equation] we can solve the BPS equations ([ref]) and ([ref]) for Higgs field $D_z̅H=0$ by [equation] with the holomorphic $N_c×N_f$ matrix $H_0$ which is called the moduli matrix [ref] .
Volume of Moduli Space of Vortex Equations and Localization · Effective Lagrangian and Moduli Space Metric · 0.82
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These higher-order corrections can, however, be systematically calculated using the approach of Ref. [ref] .
Effective field theories on solitons of generic shapes · Codimension-one case · 0.98
Compares with it 2 papers
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The former is the case of the Hanany-Tong metric [ref] (which still does not describe the correct interactions), while the latter is the case of the correct asymptotic form obtained from the BPS equations [ref] .
Group Theory of Non-Abelian Vortices · A toy metric on the vector space spanned by $| B >$ · 0.84
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Note: A week before this article was completed, a paper that contains some overlap with the material of section 7.1 in the case $Σ=$ appeared on the arXiv [ref] .
On the L^2-metric of vortex moduli spaces · Introduction · 0.86
Cites it as background 7 papers
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The moduli space metric has been found recently for well-separated vortices [ref] using a generic formula for the Kähler potential on the moduli space [ref] .
Group Theory of Non-Abelian Vortices · Introduction and discussion · 0.88
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General formula for effective Lagrangian $L_eff$ on vortices has been worked out [ref] .
Volume of Moduli Space of Vortex Equations and Localization · Effective Lagrangian and Moduli Space Metric · 0.91
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The asymptotic metric for well-separated vortices was obtained [ref] to study the low-energy scattering [ref] .
All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons · Introduction · 0.88
What it cites · 30 sentences without a confident label
Builds on 1 paper
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In this section, we consider the asymptotic form of the metric on the moduli space for $k$ well-separated non-Abelian vortices by generalizing the results for Abelian vortices [ref] .
Asymptotic Interactions of Critically Coupled Vortices · Asymptotic metric for well-separated vortices · 1.00
Compares with 1 paper
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On the other hand, the asymptotic forms of the functions[ The function $ψ_g, ψ_e$ of the $SU(N), U(1)$ parts here are related to those in Ref. [ref] by $ψ_g^here=1/N-1ψ_g^ [ref] +1/Nlog|z-z_0|^2$, and $ψ_e^here=ψ_e^ [ref] +1/Nlog|z-z_0|^2$.
Multiple Layer Structure of Non-Abelian Vortex · Single vortex configurations · 0.89
Cites as background 25 papers
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A general formula for the Kähler potential on the moduli space was obtained in [ref] .
Manifestly Supersymmetric Effective Lagrangians on BPS Solitons · Introduction · 0.83
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The moduli space of multiple vortices at arbitrary positions with arbitrary orientations in the internal space was constructed in [ref] .
Moduli Space of Non-Abelian Vortices · Introduction · 0.89
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BPS non-Abelian vortices in more general Higgs models with non-Abelian gauge symmetry were introduced in [ref] (for a review see [ref] ).
TASI Lectures on Solitons · Introduction · 0.99
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